Question: Angela has deposited $\$8,\!000$ into an account that pays $6\%$ interest compounded annually.

Bob has deposited $\$10,\!000$ into an account that pays $7\%$ simple annual interest.

In $20$ years Angela and Bob compare their respective balances. To the nearest dollar, what is the positive difference between their balances?
Solution: We may find Angela's balance by simply finding $\$8,\!000(1 + 0.06)^{20} \approx \$25,\!657.08.$

We may find Bob's balance by finding $\$10,\!000(1 + 20 \cdot 0.07) \approx \$24,\!000.$

Therefore, the difference between their balances is roughly $\$25,\!657.08 - \$24,\!000 \approx \boxed{\$1,\!657}.$